Question

The probability that a student is accepted to a prestigious college is 0.3. If 5 students from the same school apply, what is the probability that at most 4 are accepted

Answer 1

Answer:0.849185

Step-by-step explanation:

Binomial probability formula we will use:

$P(x)=\frac{n !}{x !(n-x) !} p^{x} q^{n-x}$

where,

$n=5 \\ \mathrm{P} (probability of success) =0.3 \\q=1-p$

The computation of the probability will be :

$P(x \leq 2 ; 5,0.3)=P(x=0 ; 5,0.3)+P(x=1 ; 5,0.3)+P(x=2 ; 5,0.3)+P(x=3 ; 5,0.3) \\ =\left[\frac{5 !}{5 !(5-0) !}(0.3)^{0}(1-0.3)^{5-0}\right]+\left[\frac{5 !}{5 !(5-1) !}(0.3)^{1}(1-0.3)^{5-1}\right] +\left[\frac{5 !}{5 !(5-2) !}(0.3)^{2}(1-0.3)^{5-2}\right] ++\left[\frac{5 !}{5 !(5-3) !}(0.3)^{3}(1-0.3)^{5-3}\right] ++\left[\frac{5 !}{5 !(5-4) !}(0.3)^{4}(1-0.3)^{5-4}\right] \\ =0.1681+0.3601+0.3087+0.006615+0.00567 \\ \Rightarrow 0.849185$

The probability that at most 4 are accepted = 0.849185